Sorry I missed this one somehow. I did check your site on my iPhone and experienced the same issue. I did debug the iOS browser on my Macbook Safari and see no JS errors that typically cause these issues.
Is it possible for you quickly check if disabling all plugins resolves the issue? Do make sure you do a hard refresh on the page before retesting. I see that at times a popup appears on the page when I open this page in iOS safari browser and hence there are some scripts being executed during page load.
BTW, I did check the agile demo page which has filterable portfolio – https://www.livemeshthemes.com/agile/filterable-portfolio/ and experienced no issues at all.